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DOI: 10.4230/LIPIcs.ICALP.2017.99
URN: urn:nbn:de:0030-drops-74174
URL: https://drops.dagstuhl.de/opus/volltexte/2017/7417/
Bacquey, Nicolas ; Grandjean, Etienne ; Olive, Frédéric
Definability by Horn Formulas and Linear Time on Cellular Automata
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Abstract
We establish an exact logical characterization of linear time complexity of cellular automata of dimension d, for any fixed d: a set of pictures of dimension d belongs to this complexity class iff it is definable in existential second-order logic restricted to monotonic Horn formulas with built-in successor function and d+1 first-order variables. This logical characterization is optimal modulo an open problem in parallel complexity. Furthermore, its proof provides a systematic method for transforming an inductive formula defining some problem into a cellular automaton that computes it in linear time.
BibTeX - Entry
@InProceedings{bacquey_et_al:LIPIcs:2017:7417,
author = {Nicolas Bacquey and Etienne Grandjean and Fr{\'e}d{\'e}ric Olive},
title = {{Definability by Horn Formulas and Linear Time on Cellular Automata}},
booktitle = {44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)},
pages = {99:1--99:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-041-5},
ISSN = {1868-8969},
year = {2017},
volume = {80},
editor = {Ioannis Chatzigiannakis and Piotr Indyk and Fabian Kuhn and Anca Muscholl},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2017/7417},
URN = {urn:nbn:de:0030-drops-74174},
doi = {10.4230/LIPIcs.ICALP.2017.99},
annote = {Keywords: picture languages, linear time, cellular automata of any dimension, local induction, descriptive complexity, second-order logic, horn formulas, logic }
}
| Keywords: | picture languages, linear time, cellular automata of any dimension, local induction, descriptive complexity, second-order logic, horn formulas, logic | |
| Seminar: | 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017) | |
| Issue date: | 2017 | |
| Date of publication: | 07.07.2017 |
